Vincelot, who signed on loan only yesterday from Brighton, struck after 23 minutes to get the Gills back to winning ways after a 2-1 midweek defeat at Torquay had allowed Port Vale to close the gap.
Vale came unstuck at Northampton, losing 2-0, while Torquay kept their momentum going with a second home win this week after beating Morecambe 1-0 to move into the play-off places.
Rotherham are sixth courtesy of a 1-0 home win over Plymouth, while the remainder of the chasing pack at the top of the table were unable to find their scoring boots, with Fleetwood drawing 0-0 at Rochdale and Bradford City coming up short with a 1-0 defeat at Burton Albion.
The biggest scores in a relatively quiet matchday were at Adams Park, where Wycombe succumbed 3-1 to visitors Oxford United, and Whaddon Road where defender Keith Lowe's brace helped secure a 3-0 success for Cheltenham at home to Exeter.
Barnet edged closer to fighting their way off the foot of the Football League structure after Mark Byrne's stoppage time penalty was enough to topple Chesterfield 1-0 at the Proact Stadium with Aldershot now just two points clear of the Londoners in second-bottom after a goalless draw at Dagenham.
There was one other 0-0 result, between Southend and York City at Roots Hall, while Accrington left it late to beat the out of sorts Bristol Rovers 1-0 to move up to 12th in the table.
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